Integrating problem-posing and problem-solving within mathematics teaching

The mathematical problem posing and problem solving are mutually dependent, mutually reinforcing, and develop in tandem. Over the past two decades, research on problem posing has become increasingly prevalent and in-depth among educational researchers, while research on problem solving has gradually declined. It is well known that many educational researchers have published numerous papers related to mathematical problem posing in various mathematics education research journals. Many conferences in mathematics education have also dedicated specialised discussion topics to problem posing. Educational researchers pay close attention to the solvability of problems posed by participants, employing appropriate analytical frameworks to evaluate the solvability and thereby examine participants’ problem-posing ability. However, there is a lack of research on the solutions to the problems posed by participants. Drawing upon the author's experience as a secondary school mathematics teacher, this poster presents a case study of a lesson integrating mathematical problem posing and problem solving by using a problem on set as an exemplar. In the lesson, the author and students first posed new mathematical problems based on a sample problem, then attempted to solve these newly generated problems. Research indicates that posing new problems is typically straightforward, as participants can employ a variety of problem-posing strategies. However, solving these problems can be quite challenging, often requiring mathematical knowledge and mathematical tools extending beyond the scope of secondary school mathematics, and there are very few available problem-solving strategies. Integrating problem-posing and problem-solving within mathematics teaching can foster the synergistic development of both teachers' and students' abilities in problem posing and problem solving.